Franz-Josef Brandenburg , Jean Berstel,Detlef Wotschke (editors):

Trends and Applications inFormal Language Theory

Dagstuhl-Seminar-Report; 2314.10.-18. 10.91 (9142)

ISSN 0940-1121

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Jean Berstel

Franz-Josef BrandenburgDetlef Wotschke

(editors)

Trends and Appplications in Formal Language Theory

Dagstuhl-SeminarOct. 14 - 18, 1991

Reporton the lst Dagstuhl-seminar on

Trends and Applications in Formal Language Theory

Formal language theory is one of the classical and fundamental areas of Computer Science. Formore than four decades a broad theoretical basis and a wide spectrum of applications oflanguage theory has been developed, with the l960's and l970's as the "golden age� of fonnallanguage theory. Since then other areas became more attractive to many theoretical computerscientists and research on formal languages is often presented as part of other theories. Underthis perspective the seminar on Trends and Applications in Formal Language Theory aims atserving as a forum for formal language theorists to make their research transparent as part oftheir theory.

The presented talks addressed a wide range of themes within formal language theory. Particularemphasis was laid upon the complexity of languages and their descriptions, i.e. both static anddynamic complexitytheory. A more detailed classi�cation can be done along the followingkeywords:- description complexity and general complexity- nondeterminism, unambiguity, determinism- generation of complex objects- special use of regular and context- free methods- parallel rewriting and codes

Besides the 27 presented talks there were a lot of discussions is small goups and a general one

focussing on perspectives of formal language theory. Among the participants there was a broadconsensus that the visibility of formal language theory must be improved. Activities in thisdirection of some participants were gratefully acknowledged. Clearly, the best support wouldcome from a regular conference on formal language theory or a devoted section within anestablished conference series, with Dagstuhl seminars as a first step.

All participants appreciated the stimulating Dagstuhl atmosphere and wished to thank the stafffor doing a perfect job.

Franz J. Brandenburg

Participants

Jürgen Albert, Würzburg

Jean Berstel� Paris/Frankreich

Franz-Josef Brandenburg, Passau

Anne-Brüggemann-Klein, Freiburg

Didier Caucal, R_enncs�FrankreichBruno Courcelle, Bordeaux/Frankreich

Carsten Damm, München

Jürgen Dassow� Magdeburg

Jürgen Duske, Hannover

J oaquim Gabarro, Barcelona/Spanien

Massimiliano Goldwurm, Mailand/Italien

Josef Gruska, Hamburg

Günter Hotz, Saarbrücken

Dung T. Huynh, Dallas/U SA

Birgit J enner, München

Helmut Jürgensen� London/0ntario�Kanada

Alica Kclemenova, Bratislava/CSFR

Wcmer Kuich, Wien/ÖsterreichKlaus-Jörn Lange, München

Hing Leung, Frankfurt

Jorma Rissanen� San Josö/USAJürgen Schäfer, Frankfurt

Helrnut Seidl, SaarbrückenRay Solomonoff, Saarbrücken

Wolfgang Thomas, Kiel

Paul Vitanyi, Amsterdam/Niederlande

Hermann Walter, Darmstadt

Dietrnar Wätjen, BraunschweigAndreas Weber, Frankfurt

Detlef Wotschke, Frankfurt

Abstracts

Halbringautomaten und TOL-SystemeWerner Kuich, Technische Universität Wien

Ausgangspunkt sind TOL-Systeme, deren Parallelableitungen durch Kontrollsprachen reguliertwerden. Diese werden dadurch verallgemeinert, daß formale Potenzreihen über endlichenSubstitutionen auf formale Potenzreihen über Wörtem angewendet werden. Stammen die

Potenzreihen aus abstrakten Familien von Potenzreihen (AFP), so erhält man unter gewissen

Bedingungen - als Verallgemeinerung des AFL-Resultates für ETOL-Sprachen - wieder eineAFP.

Beschränkt man sich auf algebraische Potenzreihen über N� und auf Homomorphismen, kann

man - in Verallgemeinerung von Paz, Salomaa (1973) - Wachstumsmatrizen de�nieren

und damit algebraische Potenzreihen (im Sinne der Funktionentheorie) erzeugen, die fir

gewisse kombinatorische Abzählprobleme eingesetzt werden können.

Monadic second-order de�nable graph transductions

Bruno Courcelle, Université Bordeaux

Formulas of monadic second-order logic can be used to specify graph transductions, i.e.,

multivalued functions from graphs to graphs. We obtain in this way classes of graph

transductions, called monadic second-order de�nable graph transductions (or more simply

de�nable transductions) that are closed under composition and preserve the two classes of

context- free sets of graphs, namely the class of Hyperedge Replacement (HR) and the class of

Vertex Replacement (VR) sets of graphs. These two classes can be characterized in terms of

de�nable transductions and recognizable sets of �nite trees. This characterimtion is independent

of any rewriting mechanism like the ones upon which the definitions of HR and VR grammars

are based. When restricted to words, the de�nable transductions are strictly more powerful than

the rational transductions with finite image; they do not preserve context- free languages. We

also describe the sets of discrete (edgeless) labeled graphs that are the images of HR and VR

sets under de�nable transductions: this gives a version of Parikh�s theorem (i.e., thecharacterization of the commutative images of context-free languages) which extends theclassical one and applies to HR and VR sets of graphs.

Complexities and Formal Languages - Open Questions and some new ResultsKlaus-Jiim Lange, TU München

The very deep connections between the theory of formal languages and complexity theory are 'illustrated by some typical relations between the two areas. The first part of the talk considers

complexity measures de�ned by sequential models. Using Engelfriet�s model of Automata with

Abstract Storage certain relations concerning membership and emptiness problems are derivablein a very general way. The investigation of the closure properties of complexity classes leads to

complexities of formal language operations, which are relative to pairs of complexity classes

and characterize some long standing open problems. The second part deals with parallelcomplexities. After introducing some basic modelsand their relations to sequential classes wegive more precise localizations "of formal language problems within the framework ofcomplexity classes. On the other hand, it is possible to get new characterizations of parallelmodels like CREW and EREW PRAMs by the application of some methods and notions well-knowri from formal language theory. Finally some new representations of the classes NC" andDSPACE(log n) in terms of CRCW PRAMs are obtained using notions and criteria, which

were developped in order to classify those PRAM algorithms which are effeciently

implementable on existing parallel machines.

Validating SGMLidocument grammarsAnne Briiggemann-Klein, Universität Freiburg

(joint work with Derick Wood, University of Waterloo)

A document grammar in the sense of the ISO standard 8879 on the Standard Generalized

Markup Language (SGML) is essentially a context-free grammar with rules of the formA -> [A E 1A with unique brackets [A and 1A and a regular expression E. The expression Emust be deterministic, i.e. each word can be �matched� by E in a unique way with one symbolof look-ahead.

In this talk we investigate the class of deterministic regular languages, i.e. of the languages that

can be denoted by deterministic regular expressions.

We show the following Theorem: Given a DFA M, we can decide in time quadratic in the size

of M whether the language of M is a deterministic regular language.

If the language of M is detenninistic, a deterministic expression denoting it can be constructed

from M.

Different Limitations of Lindenmayer Systems

Dietmar Wätjen, TU Braunschweig

We consider limited ETOL systems where at each step of the derivation process exactly

(a) min {k, #3, w} occurrences (#3 w being the number of occurrences of a in w)

(b) min {k, Iwl} symbolsof the word considered have to be rewritten ((a) k-limited or (b) uniformly k-limited ETOLsystems). If the value of the limitation is given by a function f: N -> No where, beginning

from the axiom, f(l) is the limitation in the first step, f(2) the limitation in the second step etc.,

then we get the defmitions of function- f-limited or uniformly function-f-limited ETOL systems.

In the non-extended case (limited TOL systems) we get a lot of incomparability results.

Especially, for different values of k, the families of (uniformly) k-limited TOL languages are

incomparable to each other.

In the extended case we get, among others, that the family of ETOL languages is strictlyincluded in the family of k-limited ETOL languages. It can be shown that every k-limited ETOL

language can be generated by a k-limited ETOL system with 2 tables, but also by a system with

at most 3 active symbols in each table.

On the contour word of polyominoes

Daniele Beauquier, Université Paris (delivered by Jean Berstel)

A polyomino is a finite union of unit cells that is homeomorphic to a disk. It can also be defined

by its contour word; the set of contour words, denoted by SC, is the set of words u ¬ C, that

have no proper factor in C, where C is the set of words w such that

lwlx = IWE and lwly = |w|;.The following are shown: Given a regular language R,

1) R n C # 0 is decidablc (due to M. Latteux)

2) R n SC at 0 is undccidablc (D. Beauquier)

3) R n CSC + 0 is decidable (D. Beauquier, M. Latteux, and K. Slowinski)Here CSC denotes the set of contour words of convex polyominoes.

A note on the degree of nondeterminism

Jürgen Dassow, TU Magdeburg (joint work with Henning Bordihn, TU Magdeburg)

Let G = (V, P, w) be a TOL system. Then the degree of nondeterminism det (G) introduced

by G. Rozenberg is defined as det(G) = maxpgp maxxgv #{zx : x �> 2x e P}.For a TOL language L, we set det(L) = min{det(G) : L = L(G)} .

Rozenberg has shown that, for any integer n, there is a TOL language Ln, such that det(L,,) =n and that det(L) S 2 holds for any ETOL language L. Clearly, an (E)TOL language is an(E)DTOL language if and only if det(L) = 1.

This measure has also been studied for k-limited L systems by Wätjen and Dassow� and it wasshown that det(L) S k for all k-limited L languages and that, for any r S k, there is a k-limited language L such that det(L,) == r.

First we mention a corresponding result for pure context-free grammars (or equivalently, OS

Systems).

�glem. i) For any n 2 l � there is a pure context-free language such that det(Ln) = n.

ii) For any context-free language, det(L) S 2.Moreover, det(L) = 1 holds if and only if L consists of a single word or L is

empty.

Analogous statements hold for other types of pure languages.Further we discuss decision problems concerning the degree of nondeterminism.

&#39;_I&#39;_h_e<m:_rg. For given TOL systems (k-limited L systems and pure context-free grammars) Gand given integer n 2 1, it is undecidable whether or not det(L(G)) = n and whether or notdet(L(G)) = det(G) ?

There is no algorithm for the computation of det(L(G)) and of a TOL system (k-limited Lsystem, pure context-free grammar) G� with L(G�) = L(G) and det(G�) = det(L(G)_).

The parallel complexity of some problems on formal languages and automata

theory

Joaquim Gabarré, LSI - UPC� Barcelona

We analyse the complexity of some problems from formal languages and automata theory. Wetake as model of computation the PRAM and the NC complexity class.

-First we study the word problem over free partially commutative groups introduced by C.

Wrathall. Our approach uses dependency graphs and associates to every group a rewriting

system over these graphs. We apply there ideas to frnd an NC algorithm.

Second we consider the word problem for free partially commutative groups. To study thisproblem we use first order logic and majority quantifrers. It is proved that it belongs to an

uniform class TC�.

Third we take the membership problem for Petri nets. As above this problem belongs to TC�class.

Finally we see, that the complexity of computing bisimulations is sequential. To do this we

reduce the circuit value problem for monotonic altemating circuits to strong-bisimilarity.

On the complexity of some finite-state automaton problems

Birgit Jenner, TU München (joint work with Carme Alvarez, UPC Barcelona)

We consider the complexity of the following functional variants of the non-emptiness problemfor nondeterrninistic (NFA) or deterministic (DFA) �nite-state automata:

(i) the ranking problem for NFA:Given an encoding of an NFA M and a word x E 2*, compute the number of words

y e L(M) with yS x;

(ii) the ranking problem for DFA;(iii) the maximal word problem �ir NFA:

Given an encoding of an NFA M and a word x E 2*, compute the maximal word y

e L(M) with y s x.

(iv) the maximal word problem for DFA.

We show, that the last problem is NSPACE(log n)-complete, while the first three are,

respectively, complete for the counting and optimization classes spanL, #L, and optL, that

we define analogously to their polynomial-time counterparts spanP, #P, and optP: Functions

l0

in #L count the number of accepting computations of an NSPACE(log n)-machine, functionsin spanL count the number of different output values of such a machine with additional output

tape, and functions in optL compute the maximum of all output values. We place the three

classes in the setting of other complexity classes and show that spanL and #P are very

similar: they share all their complete functions with respect to log-space metric-reducibility.

Consequently, the ranking problem for NFA is computable in polynomial time iff #P-�mctions

and all problems in the polynomial hierarchy are computable in polynomial time. This reveals

the hardness of spanL-functions. On the other hand, #L and optL-functions, and in particularthe ranking problem for DFA and the optimal word problem for NFA, are easy. They are not

only computable in polynomial time, but even "efficiently parallelizable�: #L C NC2 and optLC AC1. Matrix powering of positive integer matrices turns out to be #L-complete and (MAX,concat) word matrix powering optL-complete.

Buffer-Normal-Forms and synchronization of DPDAs

Jürgen Albert, Universität Würzburg

(joint work with Karel Culik II, Columbia and Juhani Karhumiiki, Turku)

We define simpli�cations of deterministic pushdown automata as a family of bijective DGSM-

mappings on the set of accepting computations. These mappings are used to remove inessentialstack-actions and to achieve several Normal-Form-properties of DPDA, e. g.- faithfulness

- no pushing e-moves

- no finite pushing

- reduced DPDAs.

It is conjectured, that a con�uence property holds forsimpli�cations and subcases are given,

where this con�uence relation is fulfilled.

Based on this claim, a second Conjecture can be concluded, namely: For synchronizable and

equivalent DPDAs M1, M2 there exists a common simplification M� for both M1 and M2.

11

Descriptions and descriptional complexity

Josef Gruska, Universität Hamburg and Slovak Academy of Sciences, Bratislava

Informatics is usually viewed as dealing primarily with computational and information

processing problems, in general. Computational complexity (broadly unterstood) is usuallyseen as perhaps the most mature part of Informatics with signi�cant impacts on mathematics.An attempt has been made in the talk to demonstrate that actually and to an increasingly large

extent Informatics is dealing with problems related to descriptions (representations,

speci�cations, declarations, languages, etc.). Descriptional complexity (broadly understood)should then be seen as an important part of complexity theory, closely related and

complementary to computational complexity, with important impacts on foundations of othersciences.

Decomposing a k-valued transducer into k unambiguous ones

Andreas Weber, Universität Frankfurt

We investigate the inner structure of finite-valued finite transducers. We show:- A k-valued

nondeterministic generalized sequential machine (NGSM) M can be effectively decomposed

into k unambiguous NGSMs M1,..., Mk such that the transduction realized by M is theunion of the transductions realized by M1,..., Mk. Each M; is of double exponential size and

can be constructed in deterministic double exponential time. By reduction, this result can be

extended to normalized finite transducers (NFTs). As a consequence, the k-valued and the k-

ambiguous NGSMs (NFTs) have the same generative power.

Influence of grammar classes to an effective description of languages

Alica Kelemenové, Slovak Academy of Sciences, Bratislava

The following results are presented:

l). For a language L, the total length of the optimal representation by CF grammars isbounded by the square of the length of its optimal representation by adult OL-systems.2) For an infinite grammar form G and the corresponding class of grammars GAG) andlanguagcs Lx(G), where x is either strict or a general interpretation, we show that for an

l2

arbitrary natural number n there is a language in Lx(G) with complexity at least n (with

respect to Gx(G)).

3) A colony of grammars is a simple grammar system consisting of regular grammars

producing �nite languages only and having the generative power of c.f. languages. For anarbitrary natural number k, there is a language which is determined by a k-element colony but

by no (k-1) element colony.

Graph acceptors and first-order logic

Wolfgang Thomas, Universität Kiel

We introduce a notion of finite state graph acceptor, which can specify "projections of local

properties� and whose expressive power matches a natural fragment of monadic second-order

logic.

The considered graphs have labelled vertices and edges (with label alphabets A, B, resp.) andare of uniformly bounded degree 5 k. A graph acceptor is given by a finite state set Q, a finite

set A of transitions (finite connected graphs with vertex labels in A X Q, edge labels in B,

and a designated center vertex), and a �constraint� (a boolean combination of conditions "there

are S n occurrences of transition 1&#39;�). A graph G with vertex set V is accepted if there exists

a �tiling t by transitions�, assigning to each vertex v a transition centered at v, such that for

some m 2 O: (1) the �m-sphere� around any v E V matches the transition of t centered at V ,

(2) the Q-components of the transitions of t define a consistent run p: V -v Q, (,3) constraintC is satis�ed for t.

Remark: Restricted to trees or words, these graph acceptors are equivalent in expressive power

to finite (tree-)automata. (Here the constraints are superfluous.)Theorem:

For any set L of finite graphs (of bounded degree S k):

(a) L is recognizable by a graph acceptor iff L is definable in existential monadic second-

order logic.

(b) L is recognizable by a single-state graph acceptor iff L is definable in first-order logic.

In the proof we use the Ehrenfeucht-Fraissé-game technique of first-order model theory, in aform due to Hanf ( 1965).

13

The complexity of Deciding Readiness & Failure Equivalence for Processes

Dung T. Huynh, University of Texas, Dallas (joint work with Lu Tian)

In this talk we present some complexity results concerning the problem of deciding readiness

and failure equivalences for �nite state processes, and recursively de�ned processes speci�edby normed context-free grammars (CFGs) in Greibach normal form (GNF). The results are as

follows. Readiness and failure equivalences for processes speci�ed by normed GNF CFGs areboth undecidable. For this class of processes, the regularity problem with respect to failure andreadiness equivalence is also undecidable. Moreover, all these undecidability results hold even

for locally unary processes. In the unary case, these problems are II2P- complete. We alsoshow that with respect to bisimulation equivalence, the regularity problem for normed GNF

CFG processes is NL-complete. Readiness and failure equivalences for �nite state processesare PSPACE-complete. This holds even for locally unary �nite state processes. These

equivalences are co-NP-complete for unary �nite state processes. Further, for acyclic �nite

state processes, readiness and failure equivalences are co-NP-complete and they are NL-

complete in the unary case. For �nite tree processes, all equivalences are L-complete.

On a_characterization of finite automata with limited nondeterminism

Hing Leung, Universität Frankfurt and New Mexico State University

In this study we want to design a new algorithmic solution to the limitedness problem on the

amount of nondeterminism in NFA. This problem is a special case of the limitedness problem

on distance automata, which has been solved independently by Hashiguchi, Leung and Simon.However, the algorithm to the general problem runs in exponential time and offers a doubleexponential upper bound on the distance when the automaton is limited in distance.

Using a new technique, we are able to derive a new characterization of �nite automata withlimited nondeterminism. From this, we deduce that if the amount of nondeterminism is

bounded then it must be S 2� -2 with the assumption that only binary branching is allowed.We conjecture that the bound could be improved to O(n).We believe that such a new technique may be extended to the study of limitedness problem for

distance automata and provide, hopefully, a single exponential upper bound on distance whichwould then imply that the limitedness problem is in PSPACE.

14

Rewriting systems and monadic theory

Didier Caucal, IRISA, Rennes

We consider the monadic second-order theory of pre�x replacement according to word

rewriting systems and tenn context-free gnammars.

The graph of the accessible pre�x transitions from a given axiom and according to a labelled

word rewriting system is effectively the transition graph of a pushdown automaton, and the

converse is true. The monadic theory of the transition graph of a pushdown automaton is

decidable (Muller and Schupp). Then the monadic theory is decidable for the�

pre�x replacement of a word rewriting system, starting from an axiom. If we do not take intoaccount the existence of an axiom, the monadic theory remains decidable because the pre�x

transition graph (not accessible) of a word rewriting system is effectively an equational graph

(in the sense of Courcelle).

The monadic theory is undecidable for the pre�x replacement according to linear context-free

grammars on terms, and to ground term rewriting systems. In spite of these strongly negative

results, we introduce a new notion on tenns with variable. A term t is entire if any subterm of

t is either a variable, or without variable, or has the same variables as t. We show that the class

of accessible pre�x transition graphs of labelled entire term of a grammar is exactly and

effectively the class of rooted equational graphs of Finite out.degree (the in.degree may be

Finite). Then, the monadic theory is decidable for the pre�x replacement according to an entireterm of a grammar, starting with an axiom. This decidability result must be extended to the non

existence of an axiom. But and on the contrary to the word case, the pre�x transition graph (not

accessible) of an entire of a grammar is generally not equational.

A Natural Generalization of Context-free Languages

Günter Hotz, Universität Saarbrücken (joint work with Yongquang Guan)

We de�ne c.f. net languages in the framework of free x-categories. These languages are special

c.f. graph languages (planar). They are closed under concatenation, star and union. It holds

Parikh�s theorem and an analog to the group invariant of the author. In the case of these

languages it is not a group but a groupoid.

The natural generalization of the c.f. word languages we get by multilinear interpretations of the

x-category applying it to the c.f. net languages. These languages have the same closure

15

properties as the net languages and the Parikh theorem holds, too. These languages form an

in�nite hierarchy depending from the maximal degree (maximal sum of inputs and outputs ofgeneraters of the x-category).

For k=l one has the tree adjoint grammars (TAG�s) of Joski. We give a simple procedure to

decide the word problem for the case k=l in time O(n5). We conjecture O(n4*2k) in thegeneral case. A more sophisticated algorithm of Guan decides the word problem in time O(n5)in case k=l.

Application of Formal Languages to Machine-Learning

Ray Solomonoff, Universität Saarbrücken

Prediction, accuracy of prediction, sample size of data needed, computational cost, and

incremental leaming are the basis of criticism of other work in Machine Learning.

A simple probablistic CFG is used to generate candidate solutions for the problem of inferring

algebraic notation from numerical examples. The technique is extended to learning to solve

linear algebraic equations and inferring the three laws of algebra.

Koza�s Genetic Algorithm for general problem solving is described. We show how algorithmic

probability can be used to improve his technique for generating new candidate solutions.

A New Approach to Formal Language Theory Using Kolmogorov Complexity

Paul Vitényi, CWI and University of Amsterdam (ioint work with Ming Li)

It is feasible to reconstruct parts of formal language theory using algorithmic complexity

(Kolmogorov complexity). We prove theorems on how to use Kolmogorov complexity, as a

concrete, powerful, tool. We do not just want to introduce fancy mathematics; our goal is to

help our readers (or listeners as the case may be) to do proofs in formal language theory in the

most essential, usually easiest, sometimes even obvious ways. We give an alternative to

pumping Lemma�s and a new characterization of regular languages in terms of Kolmogorov

complexity. We give a new quite general method to separate deterministic context free

languages and nondeterministic context free languages. We illustrate the use of the new

techniques through many examples which were considered difficult before. The approach is

16

also successful at the high end of the Chomsky hierarchy since one can quantifynonrecursiveness in terms of Kolmogorov complexity.

Hierarchies of Codes

Helmut Jiirgensen, University of Western Ontario (joint work with S.S. Yu)

It has been observed, that many natural classes of codes can be characterized as sets of

incompatible elements with respect to a binary relation on the free monoid. Indeed, very often

this relation is actually a partial ordering and, moreover, expresses certain information theoreticproperties concerning error resistance, decodability, synchronizability, etc. It turns and that the

proper setting for this correspondence is abstract dependence theory in the sense of Cohn

(�Universal Algebra�; see also Gécseg and Jiirgensen, in Algebra Universalis, to appear). A�gap theorem� explains the step within the hierarchy of codes.

Another theorem characterizes when certain subhierarchies collapse.

Tree Automata with Cost Functions, II: Polynomial Boundedness

Helmut Seidl, Universität Saarbrücken

Cost functions for finite tree automata are mappings from transitions to (tuples of) polynomials

over some semiring. We consider four semirings, namely N, the semiring of nonnegative

integers; Ä, the arctical semiring; T, the tropical semiring; and T the semiring of �nite

subsets of nonnegative integers.

We show for semirings N and A that it is decidable in polynomial time whether or not the

cost of accepting computations are bounded, and for f" that it is decidable in polynomial timewhether or not the cardinality of occuring cost sets is bounded.In all these cases we derive explicit upper bounds. For semiring �T we are able to derive similar

results at least in case of polynomials of degree at most l.

For semirings N and �Ä the methods are also applicable to get polynomial algorithms formulti-dimensional cost functions.

l7

A grammatical model for Dagstuhl seminars

Franz J . Brandenburg, Universität Passau (joint work with E1zse&#39;betCsuhaj-Varju, Budapest)

We introduce mailbox grammar systems and investigate their computational power. A mailboxgrammar system is a grammatical model for the description of cooperating and communicatingsystems. The model means that some independent agents work on global data and communicate

by exchanging messages. The data is manipulated by local replacements in order to achieve a

common goal.

Abstractly, a mailbox grammar system consists of n context-free grammers and a network for

the exchange of message. For the k-th grammar, a production is a tuple p = (r, c, E, B, A-> a,m1�...,m�), where r is the received message, c is a prefix of r and shall be consumed, E

and B are finite sets of existential and blocking context conditions, A-+ a is the context- free

core and m is the message send to the i-th agent.

We obtain a 1-1 correspondence between Turing machines and mailbox grammar systems. Asa consequence, almost all types of mailbox grammar systems are universal., generating therecursively enumerable sets.

On the size of the stack alphabet in PDAs

Dctlef Wotschke, Universität Fmnk�nrt (joint work with Jon Goldstine and John Price)

Two transformations are presented which, for any pushdown automaton (PDA) Mo with nostates and p�, stack symbols, reduce the number of stack symbols to any desired numbergreater than one. The first transformation preserves deterministic behavior and produces an

equivalent PDA with 0(nop./p) states. The second construction, using a technique which does

not preserve detenninistic behavior, produces an equivalent PDA with 0(nov/po/p) states. Bothtransformations are essentially optimal.

Minimal description length learning

Jorma Rissanen, IBM, San José

18

On ranking 1-way finitely ambiguous NL languages

Massimiliano Goldwunn, Universität Milano (joint work with Alberto Bertoni)

Given a language L C 2", the ranking problem for L consists of computing on input x e 2"the number of words y E L such that either Iyl < Ixl or lxl = Iyi and y islexicographicallylower than x. &#39;

We study the problem in the case of 1-way �nitely ambiguous NL languages showing that itbelongs to DET and hence to the class NC2. The technique is based on the use of direct sum.and Kronecker product for matrices. We also extend this result to a (apparently) larger class of

languages including the boolean closure of the class of 1-way �nitely ambiguous NL

languages.

Indexed grammars - the natural extension of contextfree grammars

Jürgen Duske, Universität Hannover

The talk gives a short overview of some results of indexed grammars which were obtained in

the last years at the Institut fur Informatik of the University of Hannover.

In 1968, Aho gave the definition of an indexed grammar, which is a slight modification of a

context-free grammar. These grammars describe the syntactic structure of their generatedlanguages in a context- free like marmer.

We introduce two modes of derivation, the V-mode (call by value) which coincides with the

original derivation mode of Aho and the R-mode (call by reference) which allows us to generate

all type-0 languages.

Self-embedding indexed grammars are considered, Chomsky-Schiitzenberger theorems forindexed and type-0 languages are given and indexed LL(k)- and strong indexed LL(k)-grammars are explained. In particular, we have that deterministic context- free languages are

exactly the right-linear indexed LL( 1)-languages.As a generalization of the iterated counter automata indexed counter languages has a lot of

interesting properties, for example, each type-0 language can be generated by an indexed

counter grammar with the R-mode of derivation, �that is each type-O language can be obtainedby counting on leftmost derivations of context-free grammars.

19

Dagstuhl-Seminar 9142 Participants

Jürgen Albert Carsten DammLehrstuhl für Informatik lI Humboldt UniversitätUniversität Würzburg Fachbereich InformatikAm Hubland Unter den Linden 6W-8700 Würzburg O-1086 BerlinGermany Germanya|bert@informatik.uni-wuerzburg.dbp.de damm@hubinf.uucpteI.: +49-931-888 5027 (5028)

and until 3/92:Jean BerstelUniversite Paris VI TU MünchenLITP Institut für InformatikInstitut Blaise Pascal Arcisstarße 214 Place Jussieu W-8000 München 275252 Paris Cedex 05 GermanyFrance damm@informatik.tu-muenchen.debersteI@Iitp.ibp.fr teI.: +49-89-2105 2397teI.: +33-1-44 77 62 42

Jürgen DassowFranz-Josef Brandenburg TU MagdeburgUniversität Passau FG Theoretische InformatikLehrstuhl für Theoretische Informatik Postfach 4120Innstraße 33 O-3010 MagdeburgW�8390 Passau Germany �Germany teI.: +37-91-5923538 / 5922759brandenb@fmi.uni-passau.deteI.: +49-851-509-343 Jürgen Duske

TU HannoverAnne Brüggemann-Klein Institut für InformatikUniversität Freiburg Welfengarten 1Institut für Informatik W-3000 Hannover 1Rheinstraße 10-12 GermanyW-7800 Freiburg teI.: +49-511-762 5184Germanybrueggemann@informatik.uni-freiburg.dbp.de Joaquim GabarroteI.: +49-761-203 3897 Universidad Politecnica de Catalunya

Facultat d�lnformaticaDidier Caucal Pau Gargallo 5Universite de Rennes E�08028 BarcelonaIRISA SpainCampus de Beaulieu gabarro@lsi.upc.esAvenue du General Leclerc teI.: +34-3-401701135042 Rennes CedexFrance Massimiliano GoldwurmcaucaI@irisa.fr Universita degli Studi di Milano

Dip. Scienze deII� lnformazioneBruno Courcelle via Comelico 39Universite Bordeaux I 20135 MilanoDepartement d�lnformatique ltaly351 Cours de la Liberation goldwurm@imiucca.csi.unimi.it23405 Talence teI.: +39-2-55 00 63 05

rance

courcelI@geocub.greco-prog.frteI.: +33-56 84 60 86

Jozef Gruska Werner KuichSlovak Academy of Sciences Technische Universität WienDepartment of Informatics Abteilung für Theoretische InformatikComputing Center Wiedner Hauptstr. 8-10Dubravaska cesta 9 A-1040 Wien842 35 Bratislava AustriaCSFR kuich@btx.uucptel; +42-7-374422 teI.: +43-1222-58801 5450an

Universität Hamburg KIaus-Jörn LangeFachbereich Informatik TU MünchenRothenbaumchaussee 67/69 Institut für InformatikW-Hamburg 13 Arcisstraße 21gruska@rosun1.informatik.uni-hamburg.de W-8000 München 2eI: +49-40-4123 5684 (5672) Germany

Iange@informatik.tu-muenchen.deGünter Hotz teI.: +49-89-2105-2403 (Secr.: 2404)Universität des SaarlandesFachbereich 14 - Informatik Hing LeungIm Stadtwald 15 _ New Mexico State UniversityW-6600 Saarbrücken 11 Department of Computer ScienceGermany Las Cruces NM 88003teI.: +49�681-302 2414 USA

hleung@nmsu.eduDung T. Huynh teI.: +1-505-646 1038The University of Texas at Dallas andComputer Science Department Universität FrankfurtBox 830688 FB Informatik (20)Richardson TX 75083 c/o Prof. WotschkeUSA Postfach 111932huynh@utdallas.edu W-6000 Frankfurt 11teI.: +1 -214-690 2169 Germany

Ieung@psc.informatik.uni-frankfurt.deBirgit Jenner teI.: +49-69-798 3976TU MünchenInstitut für Informatik Jorma RissanenArcisstr. 21 IBM Almadan Research CenterW-8000 München 2 K 52/802

Germany 650 Harry Roadjenner@informatik.tu-muenchen.de San Jose CA 95120-6099teI.: +49�89-2105-2387 USA

rissanen@ibm.comHelmut JurgensenUniversity of Western Ontario Jürgen SchäferDepartment of Computer Science Hoechst AGMiddlesex College Aus- und WeiterbildungLondon Ontario N6A 5B7 Computer LernzentrumCanada W-6230 FrankfurtheImut@uwo.ca GermanyteI.: +1 -519-661-3560 teI.: +49�69-305 733

Alica Kelemenova Helmut Seidl -Slovak Academy of Sciences Universität SaarbrückenDepartment of Informatics Fachbereich 14 - InformatikComputing Center u Im Stadtwald 15Dubravaska cesta 9 W-6600 Saarbrücken 11842 35 Bratislava GermanyCSFR seidl@sol.cs.uni�sb.deteI.: +42-7-375859 teI.: +49-681-302 2454

Ray J. Solomonoff Detlef WotschkeUniversität des Saarlandes Universität FrankfurtFachbereich 14 - Informatik Fachbereich Informatik (20)Im Stadtwald 15 Robert-Mayer-Str. 11-15W-6600 Saarbrücken 11 W-6000 Frankfurt 11Germany Germanyinfi@cs.uni-sb.de wotschke@psc.informatik.uni-frankfurt.deteI.: +49-681-302 6389 teI.: +49-69-798 3800

Wolfgang ThomasUniversität KielInstitut für InformatikOlshausenstraße 40W-2300 Kiel 1

Germanywt@informatik.uni-kieI.dbp.deteI.: +49-431-880 4480

Paul VitanyiCWI - Mathematisch CentrumKruislaan 413NL-1098 SJ AmsterdamThe Netherlands

pauIv@cwi.nIteI.: +31�20-592 4124

Dietmar WätjenTU BraunschweigInstitut für Theoretische InformatikGau ßstr. 11

W-3300 BraunschweigGermanywaetjen@infbs.uucpteI.: +49-531 -391 2387

Hermann WalterTechnische Hochschule DarmstadtInstitut für Theoretische InformatikFrankfurter Str. 69 AW-61 O0 Darmstadt

Germanyxitimskr@ddathd21 .bitnetteI.: +49-6151-16 34 05/16 48 95

Egon Wanke -Universität GH PaderbornFB 17 - Mathematik/Informatik

Warburgerstr. 100W-4790 Paderborn

Germanyegon@uni-paderborn.deteI.: +49-5251 -60 30 74

Andreas WeberUniversität FrankfurtFachbereich Informatik (20)Robert-Mayer-Str. 11-15W-6000 Frankfurt 11Germanyweber@psc.informatikuni-frankfurt.deteI.: +49-69-798 8176

Bisher erschienene und geplante Titel:

W. Gentzsch, W.J. Paul (editors):Architecture and Performance, Dagstuhl-Seminar-Report; 1, 18.-20.6.1990; (9025)

K. Harbusch, W. Wahlster (editors):Tree Adjoining Grammars, lst. Intemational Worshop on TAGS: Formal Theory and Ap-plications, Dagstuhl-Seminar-Report; 2, 15.-17.8.1990 (9033)

Ch. Hankin, R. Wilhelm (editors):Functional Languages: Optimization for Parallelism, Dagstuhl-Seminar-Report; 3, 3.-7.9.1990 (9036)

H. Alt, E. Welzl (editors):Algorithmic Geometry, Dagstuhl-Seminar-Report; 4, 8.-12. 10.1990 (9041)

J. Berstel , J .E. Pin, W. Thomas (editors):Automata Theory and Applications in Logic and Complexity, Dagstuhl-Seminar-Report;5, 14.-18.1. 1991 (9103)

B. Becker, Ch. Meinel (editors):Entwerfen, Prüfen, Testen, Dagstuhl-Seminar-Report; 6, 18.-22.2.1991 (9108)

J . P. Finance, S. Jiihnichen, J . Loeckx, M. Wirsing (editors):Logical Theory for Program Construction, Dagstuhl-Seminar-Report; 7, 25.2.-1.3.1991(9109)

E. W. Mayr, F. Meyer auf der Heide (editors):Parallel and Distributed Algorithms, Dagstuhl-Seminar-Report-; 8, 4.-8.3.1991 (9110)

M. Broy, P. Deussen, E.-R. Olderog, W.P. de Roever (editors):Concurrent Systems: Semantics, Specification, and Synthesis, Dagstuhl-Seminar-Report;9, 11.-15.3.1991 (9111)

K. Apt, K. Indermark, M. Rodriguez-Artalejo (editors):Integration of Functional and Logic Programming, Dagstuhl-Seminar-Report; l0, 18.-22.3.1991 (9112)

E. Novak, J . Traub, H. Wozniakowski (editors):Algorithms and Complexity for Continuous Problems, Dagstuhl-Seminar-Report; 11, 15-19.4.1991 (9116)

B. Nebel, C. Peltason, K. v. Luck (editors):Terminological Logics, Dagstuhl-Seminar-Report; 12, 6.5.-18.5.1991 (9119)

R. Giegerich, S. Graham (editors):Code Generation - Concepts, Tools, Techniques, Dagstuhl-Seminar-Report; 13, 20.-24.5.1991 (9121)

M. Karpinski, M. Luby, U. Vazirani (editors):Randomized Algorithms, Dagstuhl-Seminar-Report; 14, 10.-14.6.1991 (9124)

J. Ch. Freytag, D. Maier, G. Vossen (editors):Query Processing in Object-Oriented, Complex-Object and Nested Relation Databases,Dagstuhl-Seminar-Report; 15, 17.-21.6.1991 (9125)

M. Droste, Y. Gurevich (editors):Semantics of Programming Languages and Model Theory, Dagstuhl-Seminar-Report; 16,24.-28.6.1991 (9126)

G. Farin, H. Hagen, H. Noltemeier (editors):Geometric Modelling, Dagstuhl-Seminar-Report; 17, 1.-5.7.1991 (9127)

A. Karshmer, J. Nehmer (editors):Operating Systems of the 1990s, Dagstuhl-Seminar-Report; 18, 8.-12.7.1991 (9128)

H. Hagen, H. Müller, G.M. Nielson (editors):Scientific Visualization, Dagstuhl-Seminar-Report; 19, 26.8.-30.8.91 (9135)

T. Lengauer, R. Möhring, B. Preas (editors):Theory and Practice of Physical Design of VLSI Systems, Dagstuhl-Seminar-Report; 20,2.9.�6.9.9l (9136)

F. Bancilhon, P. Lockemann, D. Tsichritzis (editors):Directions of Future Database Research, Dagstuhl-Seminar-Report; 21, 9.9.-12.9.91(9137)

H. Alt, B. Chazelle, E. Welzl (editors):Computational Geometry, Dagstuhl-Seminar-Report; 22, 07.10.-11.10.91 (9141)

F.J. Brandenburg , J. Berstel, D. Wotschke (editors): 9Trends and Applications in Formal Language Theory, Dagstuhl-Seminar-Report; 23,14.10.-18.10.91 (9142)

H. Comon , H. Ganzinger, C. Kirchner, H. Kirchner, J .-L. Lassez , G. Smolka (editors):Theorem Proving and Logic Programming with Constraints, Dagstuhl-Seminar-Report;24, 21.10.-25.10.91 (9143)

H. Noltemeier, T. Ottmann, D. Wood (editors):Data Structures, Dagstuhl-Seminar-Report; 25, 4.11.-8.11.91 (9145)

A. Dress, M. Karpinski, M. Singer(editors):Efficient Interpolation Algorithms, Dagstuhl-Seminar-Report; 26, 2.-6. 12.91 (9149)

B. Buchberger, J . Davenport, F. Schwarz (editors):Algorithms of Computeralgebra, Dagstuhl-Seminar-Report; 27, 16..-20.12.91 (9151)

K. Compton, J .E. Pin , W. Thomas (editors): Automata Theory: In�nite Computations, Dagstuhl-Seminar-Report; 28, 6.�lO.l.92 (9202)

H. Langmaack, E. Neuhold, M. Paul (editors): Software Construction - Foundation and Applica-tion, Dagstuhl-Seminar-Report; 29, 13..-17.1.92 (9203)

K. Ambos-Spies, S. Homer, U. Schöning (editors): Structure and Complexity Theory, Dagstuhl-Seminar-Report; 30, 3.-7.02.92 (9206)

B. Booß, W. Coy, J .-M. Pfliiger (editors): Limits of Modelling with Programmed Machines, Dag-stuhl-Seminar-Report; 31, 10.-14.2.92 (9207)